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Two physicists map where to park your car, according to mathematics

Physicists Paul Krapivsky (Boston University) and Sidney Redner (Santa Fe Institute) decided to use math to answer an old question: where is the best place to park your car. The criteria? To find the parking space for that minimizes the time spent on the lot.

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Intelligent Decision

"Mathematics lets you make intelligent decisions," Redner said. "It allows you to approach a complex world with little insight."

In his new study, physicists chart three simple parking strategies in an idealized parking area with a row. They call their strategies; humble, optimistic and cautious.

Certainly refers to drivers who grab hold of the first available space. Optimistic indicates the drivers who are playing to find a space next to the entrance. At the same time, caution refers to when the drivers take the middle route.

The authors used several techniques to calculate the relative benefits of each strategy. To begin with, the humble strategy reflected a dynamic seen in the microtubules that provide scaffolding within living cells. They therefore used an equation describing a microtubule length to calculate the chain of "humble" cars at the bottom of the lot.

"Sometimes there are connections between things that seem to have no connection," Redner said. "In this case, the connection to microtubule dynamics made the problem solvable."

The optimistic strategy was described by a differential equation, and the cautious strategy was represented by a simulation that allowed physicists to calculate the average density of spots and the amount of backtracking required.

Sustainable strategy wins

In the end, the cautious strategy followed closely by the optimistic strategy.

However, Redner acknowledges that his approach sacrifices real application in exchange for mathematical insight. "If you really want to become an engineer, you have to take into account how fast people drive, the actual layout of the parking lot and the seats – all these things," he commented.

"When you start to be completely realistic, [every parking situation is different] and you lose the opportunity to explain something."

Still, for Redner, the exercise was about the joy of thinking analytically about everyday situations.

"We live in a crowded society, and we always encounter the congestion phenomenon in parking lots, traffic patterns, you say," he said. "If you can look at it with the right eyes, you can account for something."

The research is published in this week's Journal of Statistical Mechanics .

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